Firefighting is a substantially more intensive job then you give it credit for and the vast majority of the population would not be well suited to carrying out all the tasks a firefighter needs to do. The protective suits are 50 pounds on their own, let alone the weight of oxygen tanks, miscellaneous gear, and hoses. Carrying all that and then potentially a whole person in a hellish deadly scenario while not panicking takes a massive amount of training, strength, and resolve.
Societies function far better with specialization anyway, sending an engineer onto trash duty feels like a waste of resources.